Spectrum sensing is a key function for Cognitive Radio (CR) systems. In order to provide flexible spectrum-sensing resolutions, a wavelet basis may be used in order to adjust one or more spectrum-sensing resolutions. Prior wavelet generators used in generating the wavelet basis are limited in that they must individually store a plurality of predetermined wavelet bases or otherwise cannot easily change the resolution of the wavelet basis. Moreover, these prior wavelet generators oftentimes require complex hardware that may involve significant costs and processing time. Accordingly, there is a need in the industry for a more flexible digital wavelet generator.